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On Some Problems in Lagrangian Dynam...
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ProQuest Information and Learning Co.
On Some Problems in Lagrangian Dynamics and Finsler Geometry.
Record Type:
Language materials, manuscript : Monograph/item
Title/Author:
On Some Problems in Lagrangian Dynamics and Finsler Geometry./
Author:
Chen, Dong.
Description:
1 online resource (52 pages)
Notes:
Source: Dissertation Abstracts International, Volume: 79-04(E), Section: B.
Contained By:
Dissertation Abstracts International79-04B(E).
Subject:
Theoretical mathematics. -
Online resource:
click for full text (PQDT)
ISBN:
9780355329940
On Some Problems in Lagrangian Dynamics and Finsler Geometry.
Chen, Dong.
On Some Problems in Lagrangian Dynamics and Finsler Geometry.
- 1 online resource (52 pages)
Source: Dissertation Abstracts International, Volume: 79-04(E), Section: B.
Thesis (Ph.D.)
Includes bibliographical references
The purpose of this dissertation is to present several applications of enveloping functions and dual lens maps to geometry and dynamical systems. In Chapter 1 we have a brief review on basic notions and theory we need to understand the main results. In Chapter 2 we prove that given a point on a Finsler surface, one can always find a neighborhood of the point and isometrically embed this neighborhood into a Finsler torus without conjugate points. The major tool is enveloping functions.
Electronic reproduction.
Ann Arbor, Mich. :
ProQuest,
2018
Mode of access: World Wide Web
ISBN: 9780355329940Subjects--Topical Terms:
1180455
Theoretical mathematics.
Index Terms--Genre/Form:
554714
Electronic books.
On Some Problems in Lagrangian Dynamics and Finsler Geometry.
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Chen, Dong.
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On Some Problems in Lagrangian Dynamics and Finsler Geometry.
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2017
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1 online resource (52 pages)
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Source: Dissertation Abstracts International, Volume: 79-04(E), Section: B.
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Adviser: Dmitri Burago.
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Thesis (Ph.D.)
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The Pennsylvania State University
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2017.
504
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Includes bibliographical references
520
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The purpose of this dissertation is to present several applications of enveloping functions and dual lens maps to geometry and dynamical systems. In Chapter 1 we have a brief review on basic notions and theory we need to understand the main results. In Chapter 2 we prove that given a point on a Finsler surface, one can always find a neighborhood of the point and isometrically embed this neighborhood into a Finsler torus without conjugate points. The major tool is enveloping functions.
520
$a
In Chapter 3 we introduce the dual lens map technique developed by Burago and Ivanov. It derives from enveloping functions and symplectic geometry. We then show how this technique is used to perturb the geodesic flows of flat Finsler tori.
520
$a
In Chapter 4 we show how dual lens map can be used in KAM theory. The celebrated KAM Theory says that if one makes a small perturbation of a nondegenerate completely integrable system, we still see a huge measure of invariant tori with quasi-periodic dynamics in the perturbed system. These invariant tori are known as KAM tori. What happens outside KAM tori draws a lot of attention. We show two types of Lagrangian perturbations of the geodesic flow on flat Finsler tori. The perturbations are Cinfinity small but the resulting flows has a positive measure of trajectories with positive Lyapunov exponent. The measure of this set is of course extremely small. Still, the flow has positive metric entropy. From this result we get positive metric entropy outside some KAM tori and it gives positive answer to a question asked by Kolmogorov.
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Electronic reproduction.
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Ann Arbor, Mich. :
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ProQuest,
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2018
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Mode of access: World Wide Web
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Theoretical mathematics.
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1180455
655
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Electronic books.
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local
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554714
690
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ProQuest Information and Learning Co.
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The Pennsylvania State University.
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Dissertation Abstracts International
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79-04B(E).
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http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=10666452
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click for full text (PQDT)
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